Properties

Label 3311.1
Level 3311
Weight 1
Dimension 406
Nonzero newspaces 11
Newforms 36
Sturm bound 887040
Trace bound 2

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Defining parameters

Level: \( N \) = \( 3311 = 7 \cdot 11 \cdot 43 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 11 \)
Newforms: \( 36 \)
Sturm bound: \(887040\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3311))\).

Total New Old
Modular forms 5510 4098 1412
Cusp forms 470 406 64
Eisenstein series 5040 3692 1348

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 406 0 0 0

Trace form

\( 406q + 4q^{2} + 30q^{4} + 2q^{7} - 2q^{8} + 30q^{9} + O(q^{10}) \) \( 406q + 4q^{2} + 30q^{4} + 2q^{7} - 2q^{8} + 30q^{9} - 2q^{11} - 12q^{14} - 8q^{15} + 12q^{16} - 6q^{18} + 4q^{22} + 8q^{23} + 30q^{25} - 4q^{28} + 4q^{29} - 50q^{32} + 30q^{36} - 6q^{37} + 2q^{43} - 4q^{44} - 2q^{46} + 32q^{49} + 4q^{50} - 18q^{53} - 52q^{56} - 6q^{58} - 24q^{60} + 2q^{63} + 16q^{64} - 8q^{67} - 6q^{71} - 2q^{72} - 34q^{74} + 2q^{77} - 16q^{78} - 6q^{79} + 30q^{81} - 39q^{86} - 23q^{88} - 8q^{92} + 4q^{98} - 12q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3311))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
3311.1.b \(\chi_{3311}(386, \cdot)\) None 0 1
3311.1.d \(\chi_{3311}(1506, \cdot)\) None 0 1
3311.1.f \(\chi_{3311}(1420, \cdot)\) None 0 1
3311.1.h \(\chi_{3311}(3310, \cdot)\) 3311.1.h.a 1 1
3311.1.h.b 1
3311.1.h.c 1
3311.1.h.d 1
3311.1.h.e 1
3311.1.h.f 1
3311.1.h.g 2
3311.1.h.h 2
3311.1.h.i 2
3311.1.h.j 2
3311.1.h.k 3
3311.1.h.l 3
3311.1.h.m 3
3311.1.h.n 3
3311.1.h.o 6
3311.1.h.p 6
3311.1.o \(\chi_{3311}(2199, \cdot)\) None 0 2
3311.1.q \(\chi_{3311}(2157, \cdot)\) None 0 2
3311.1.s \(\chi_{3311}(122, \cdot)\) None 0 2
3311.1.t \(\chi_{3311}(472, \cdot)\) None 0 2
3311.1.u \(\chi_{3311}(824, \cdot)\) None 0 2
3311.1.v \(\chi_{3311}(2014, \cdot)\) None 0 2
3311.1.y \(\chi_{3311}(474, \cdot)\) None 0 2
3311.1.z \(\chi_{3311}(1671, \cdot)\) None 0 2
3311.1.bb \(\chi_{3311}(639, \cdot)\) None 0 2
3311.1.bd \(\chi_{3311}(1033, \cdot)\) None 0 2
3311.1.be \(\chi_{3311}(681, \cdot)\) None 0 2
3311.1.bg \(\chi_{3311}(2531, \cdot)\) None 0 2
3311.1.bj \(\chi_{3311}(1332, \cdot)\) None 0 2
3311.1.bl \(\chi_{3311}(2573, \cdot)\) None 0 2
3311.1.bm \(\chi_{3311}(1770, \cdot)\) 3311.1.bm.a 2 2
3311.1.bm.b 2
3311.1.bo \(\chi_{3311}(2113, \cdot)\) None 0 2
3311.1.bq \(\chi_{3311}(601, \cdot)\) 3311.1.bq.a 4 4
3311.1.bq.b 4
3311.1.bs \(\chi_{3311}(818, \cdot)\) None 0 4
3311.1.bu \(\chi_{3311}(904, \cdot)\) None 0 4
3311.1.bw \(\chi_{3311}(687, \cdot)\) None 0 4
3311.1.bx \(\chi_{3311}(538, \cdot)\) 3311.1.bx.a 6 6
3311.1.bx.b 6
3311.1.bz \(\chi_{3311}(188, \cdot)\) None 0 6
3311.1.cb \(\chi_{3311}(274, \cdot)\) None 0 6
3311.1.cd \(\chi_{3311}(309, \cdot)\) None 0 6
3311.1.cm \(\chi_{3311}(251, \cdot)\) 3311.1.cm.a 8 8
3311.1.cm.b 8
3311.1.co \(\chi_{3311}(811, \cdot)\) 3311.1.co.a 8 8
3311.1.co.b 8
3311.1.cp \(\chi_{3311}(436, \cdot)\) None 0 8
3311.1.cr \(\chi_{3311}(214, \cdot)\) None 0 8
3311.1.cu \(\chi_{3311}(93, \cdot)\) None 0 8
3311.1.cw \(\chi_{3311}(79, \cdot)\) None 0 8
3311.1.cx \(\chi_{3311}(431, \cdot)\) None 0 8
3311.1.cz \(\chi_{3311}(37, \cdot)\) None 0 8
3311.1.db \(\chi_{3311}(437, \cdot)\) None 0 8
3311.1.dc \(\chi_{3311}(388, \cdot)\) None 0 8
3311.1.df \(\chi_{3311}(509, \cdot)\) None 0 8
3311.1.dg \(\chi_{3311}(222, \cdot)\) None 0 8
3311.1.dh \(\chi_{3311}(171, \cdot)\) None 0 8
3311.1.di \(\chi_{3311}(423, \cdot)\) None 0 8
3311.1.dk \(\chi_{3311}(295, \cdot)\) None 0 8
3311.1.dm \(\chi_{3311}(337, \cdot)\) None 0 8
3311.1.dp \(\chi_{3311}(111, \cdot)\) None 0 12
3311.1.dr \(\chi_{3311}(76, \cdot)\) 3311.1.dr.a 12 12
3311.1.dr.b 12
3311.1.ds \(\chi_{3311}(186, \cdot)\) None 0 12
3311.1.du \(\chi_{3311}(254, \cdot)\) None 0 12
3311.1.dx \(\chi_{3311}(331, \cdot)\) None 0 12
3311.1.dz \(\chi_{3311}(109, \cdot)\) None 0 12
3311.1.ea \(\chi_{3311}(219, \cdot)\) None 0 12
3311.1.ec \(\chi_{3311}(177, \cdot)\) None 0 12
3311.1.ee \(\chi_{3311}(241, \cdot)\) None 0 12
3311.1.ef \(\chi_{3311}(551, \cdot)\) None 0 12
3311.1.ei \(\chi_{3311}(705, \cdot)\) None 0 12
3311.1.ej \(\chi_{3311}(362, \cdot)\) None 0 12
3311.1.ek \(\chi_{3311}(131, \cdot)\) None 0 12
3311.1.el \(\chi_{3311}(353, \cdot)\) None 0 12
3311.1.en \(\chi_{3311}(155, \cdot)\) None 0 12
3311.1.ep \(\chi_{3311}(197, \cdot)\) None 0 12
3311.1.er \(\chi_{3311}(113, \cdot)\) None 0 24
3311.1.et \(\chi_{3311}(127, \cdot)\) None 0 24
3311.1.ev \(\chi_{3311}(97, \cdot)\) 3311.1.ev.a 24 24
3311.1.ev.b 24
3311.1.ex \(\chi_{3311}(118, \cdot)\) 3311.1.ex.a 24 24
3311.1.ex.b 24
3311.1.fd \(\chi_{3311}(57, \cdot)\) None 0 48
3311.1.ff \(\chi_{3311}(71, \cdot)\) None 0 48
3311.1.fh \(\chi_{3311}(124, \cdot)\) None 0 48
3311.1.fi \(\chi_{3311}(94, \cdot)\) None 0 48
3311.1.fj \(\chi_{3311}(61, \cdot)\) None 0 48
3311.1.fk \(\chi_{3311}(31, \cdot)\) None 0 48
3311.1.fn \(\chi_{3311}(47, \cdot)\) None 0 48
3311.1.fo \(\chi_{3311}(19, \cdot)\) None 0 48
3311.1.fq \(\chi_{3311}(158, \cdot)\) None 0 48
3311.1.fs \(\chi_{3311}(107, \cdot)\) None 0 48
3311.1.ft \(\chi_{3311}(74, \cdot)\) None 0 48
3311.1.fv \(\chi_{3311}(114, \cdot)\) None 0 48
3311.1.fy \(\chi_{3311}(137, \cdot)\) None 0 48
3311.1.ga \(\chi_{3311}(95, \cdot)\) None 0 48
3311.1.gb \(\chi_{3311}(62, \cdot)\) 3311.1.gb.a 48 48
3311.1.gb.b 48
3311.1.gd \(\chi_{3311}(146, \cdot)\) 3311.1.gd.a 48 48
3311.1.gd.b 48

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3311))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3311)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(301))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(473))\)\(^{\oplus 2}\)